Classification of minimal surface forms for architectural application /
To understand any phenomena it is necessary to classify them on the basis of the properties they share. This dissertation deals with the generation of a very wide range of minimal surface forms and categorizes them according to their sequence of evolution and their geometrical and physical propertie...
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| Format: | Thesis Book |
| Language: | English |
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[College Station, Tex.] :
Chowdhury,
1977.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=756487771&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | To understand any phenomena it is necessary to classify them on the basis of the properties they share. This dissertation deals with the generation of a very wide range of minimal surface forms and categorizes them according to their sequence of evolution and their geometrical and physical properties which include the number of internal edges of intersection, vertexes, planes of symmetry, axis of rotation, ratio and proportions, approximate areas, etc. These forms are arranged in the different plates ac-cording to their progressive development due to (1) the gradual increment or reduction in the complexity of their boundary configuration within the generating framework, which in many cases involves the gradual increase or reduction in the number of sides of the generating framework, and (2) the gradual change in the proportion of the generating framework. Since the number of minimal surface forms which can be generated is infinite, in this dissertation only those forms of more probable architectural significance are illustrated in some detail. The forms are first classified into two primary divisions, bubbles and membranes. The bubble is that form which encloses a volume using only the minimum area of its surface to do so. Membranes are those forms generated when a surface spans a closed boundary in space, and they may consist of one or more branching surfaces depending on the configuration of the framework within which they are generated. The two primary divisions are then subdivided according to the special conditions under which they are formed and the resultant forms are recorded. For example, bubble forms are classified as free bubbles, bubbles floating on one surface, bubbles inside parallel plates, bubbles inside circular or prismatic tubes, bubbles on double curved surfaces, or bubbles inside separate or continuous frameworks. The membrane forms are classified on the basis of the conditions in which they are formed such as inside a continuous framework, inside separated frame-work, or through a set of points. Special emphasis is given to those forms which are generated inside regular polyhedral frameworks. Two charts are enclosed at the back of the dissertation showing in one the minimal surface membrane forms that are generated inside regular solid frame-works arranged according to the sequence of the development of their generating frameworks, and in the other chart, the classification of bubble forms on the basis of five special conditions under which they are formed. The properties of minimal surface forms can be summed up in three main points. (1) The surface area is minimum to span a particular boundary or to enclose a particular volume. (2) At any point on the surface the sum of positive and negative radii of curvature is constant, in the case of membrane the sum is zero and in the case of bubble it is usually other than zero. (3) The tension in the surface is constant in all directions throughout the surface. The architectural application of minimal surfaces is unique in the characteristic of independence from gravity, being stabilized only by the geometric shape and the ability to transfer all applied forces throughout the structure in pure tension. |
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| Item Description: | Vita. "Major subject: Architecture." |
| Physical Description: | xiii, 97 leaves : illustrations ; 28 cm. |
| Bibliography: | Bibliography: leaf 80. |